Encyclopedia of Microtonal Music Theory

tolerance

Irrational [musical] intervals, like those found in ETs, can be concordant when they are close in size to rational intervals. A definition of accordance based on properties of rational numbers can be adapted to explain this by including a tolerance funtion. Everybody's favorite is Paul Erlich's Harmonic Entropy, which, along the way, explains one of the reasons why small-numbered ratios are consonant in the first place.

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